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Intercepts & Slopes
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Intercepts y-intercept N x-intercept Intercepts and Slopes STUDY GUIDE Finding Intercepts ● If solving for x-intercepts, plug y = 0 into the equation and solve for x. The point will be in the form (x, 0). 1.Solve for the x-intercept 。 Set y = 0. o 2x - 3(0) = 6 o 2x0= 6 o 2x = 6 6 2 • If solving for x-intercepts, plug x = 0 into the equation and solve for y. The point will be in the form (0, y). 0 X = x-intercepts: the points on the graph that cross the x-axis (y = 0) EX. Solve for the x-intercept and y-intercept of the equation: 2x - 3y = 6. = 3 y-intercepts: the points on the graph that cross the x-axis (x = 0) 2. Solve for the y-intercept o Set x = 0. 2(0) - 3y = 6 。 0-3y = 6 。 -3y = 6 6 -3 o y = So, the x-intercept is (3, 0) and the y-intercept is (0, -2). = -2 Slopes • Definition: slope measures the "steepness" of a line. It is the ratio of the change in y (vertical change) to the change in x (horizontal change) between two points on the line. • Formula: To find the slope m between two points (x₁, y₁) and (x2, Y2): (y2 - y₁) (x2-x1) Slope-Intercept Form: The equation of a line in slope-intercept form is ● ● ● where: om is the slope of the line ob...
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Alternative transcript:
is the y-intercept Signs of Slope (+ or -): m= Special Slopes: o horizontal lines have a slope of 0. o vertical lines have an undefined slope. * Positive Slope (uphill) y = mx + b, Negative Slope (downhill) EX. Calculate the slope between the points (3, 4) and (7, 1). Use the following formula for slope: We are given that: • Y₁ = 4, x₁ = 3, y₂ = 1, X₂ = 7 Plugging in, we get: m = m = (y2 - Y1) (x₂-x1) EX. Graph the equation: y = -2x + 5. -5 Let's follow the steps outlined above. a. Using slope: • Start at the y-intercept, (0, 5). (Y2 - Y₁) (x2-x1) = Graphing Linear Equations 1.Plot the y intercept. 2. Use the slope to find additional points. 3. Continue this process to plot more points, and you'll get a straight line. (1-4) (7-3) -1 -1 -3 = -5 -3 4 y-intercept • Use the slope of -2 to go down 2 units (negative because of the slope) and right 1 unit from the y-intercept to find another point: (1, 3). ● -1 -2 Practice Problems -3 -4 -5 Continue this process until a straight line can be drawn. -1 -2 -3 -4 (1, 3) -5 1. Find the x-intercept and y-intercept of the equation: 4x + 2y = 12. 2. Write the equation of a line with a slope of 1/2 and a y-intercept of 3. 3.Calculate the slope between the points (5, -3) and (1, 7). 4.Graph the equation: y = 2x - 1.
Detailed study guide of intercepts, slopes, and graphing linear equations. Includes examples and pracrice problems.
priscilla
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Detailed study guide of intercepts, slopes, and graphing linear equations. Includes examples and pracrice problems.
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Intercepts y-intercept N x-intercept Intercepts and Slopes STUDY GUIDE Finding Intercepts ● If solving for x-intercepts, plug y = 0 into the equation and solve for x. The point will be in the form (x, 0). 1.Solve for the x-intercept 。 Set y = 0. o 2x - 3(0) = 6 o 2x0= 6 o 2x = 6 6 2 • If solving for x-intercepts, plug x = 0 into the equation and solve for y. The point will be in the form (0, y). 0 X = x-intercepts: the points on the graph that cross the x-axis (y = 0) EX. Solve for the x-intercept and y-intercept of the equation: 2x - 3y = 6. = 3 y-intercepts: the points on the graph that cross the x-axis (x = 0) 2. Solve for the y-intercept o Set x = 0. 2(0) - 3y = 6 。 0-3y = 6 。 -3y = 6 6 -3 o y = So, the x-intercept is (3, 0) and the y-intercept is (0, -2). = -2 Slopes • Definition: slope measures the "steepness" of a line. It is the ratio of the change in y (vertical change) to the change in x (horizontal change) between two points on the line. • Formula: To find the slope m between two points (x₁, y₁) and (x2, Y2): (y2 - y₁) (x2-x1) Slope-Intercept Form: The equation of a line in slope-intercept form is ● ● ● where: om is the slope of the line ob...
Intercepts y-intercept N x-intercept Intercepts and Slopes STUDY GUIDE Finding Intercepts ● If solving for x-intercepts, plug y = 0 into the equation and solve for x. The point will be in the form (x, 0). 1.Solve for the x-intercept 。 Set y = 0. o 2x - 3(0) = 6 o 2x0= 6 o 2x = 6 6 2 • If solving for x-intercepts, plug x = 0 into the equation and solve for y. The point will be in the form (0, y). 0 X = x-intercepts: the points on the graph that cross the x-axis (y = 0) EX. Solve for the x-intercept and y-intercept of the equation: 2x - 3y = 6. = 3 y-intercepts: the points on the graph that cross the x-axis (x = 0) 2. Solve for the y-intercept o Set x = 0. 2(0) - 3y = 6 。 0-3y = 6 。 -3y = 6 6 -3 o y = So, the x-intercept is (3, 0) and the y-intercept is (0, -2). = -2 Slopes • Definition: slope measures the "steepness" of a line. It is the ratio of the change in y (vertical change) to the change in x (horizontal change) between two points on the line. • Formula: To find the slope m between two points (x₁, y₁) and (x2, Y2): (y2 - y₁) (x2-x1) Slope-Intercept Form: The equation of a line in slope-intercept form is ● ● ● where: om is the slope of the line ob...
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Alternative transcript:
is the y-intercept Signs of Slope (+ or -): m= Special Slopes: o horizontal lines have a slope of 0. o vertical lines have an undefined slope. * Positive Slope (uphill) y = mx + b, Negative Slope (downhill) EX. Calculate the slope between the points (3, 4) and (7, 1). Use the following formula for slope: We are given that: • Y₁ = 4, x₁ = 3, y₂ = 1, X₂ = 7 Plugging in, we get: m = m = (y2 - Y1) (x₂-x1) EX. Graph the equation: y = -2x + 5. -5 Let's follow the steps outlined above. a. Using slope: • Start at the y-intercept, (0, 5). (Y2 - Y₁) (x2-x1) = Graphing Linear Equations 1.Plot the y intercept. 2. Use the slope to find additional points. 3. Continue this process to plot more points, and you'll get a straight line. (1-4) (7-3) -1 -1 -3 = -5 -3 4 y-intercept • Use the slope of -2 to go down 2 units (negative because of the slope) and right 1 unit from the y-intercept to find another point: (1, 3). ● -1 -2 Practice Problems -3 -4 -5 Continue this process until a straight line can be drawn. -1 -2 -3 -4 (1, 3) -5 1. Find the x-intercept and y-intercept of the equation: 4x + 2y = 12. 2. Write the equation of a line with a slope of 1/2 and a y-intercept of 3. 3.Calculate the slope between the points (5, -3) and (1, 7). 4.Graph the equation: y = 2x - 1.