## The slope Intercept form of the equation of a line that passes through point ( 2.-13) Is y =5x – 3. What is the point-slope form of the equa

Question

The slope Intercept form of the equation of a line that passes through point ( 2.-13) Is y =5x – 3. What is the point-slope form of the equation for this line?​

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2 weeks 2021-09-13T14:22:10+00:00 1 Answer 0

1. The point-slope form of the equation for this line is y + 13 = 5(x + 2)

Step-by-step explanation:

Let us revise the slope-intercept form and the point-slope form

of an equation

• The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept
• The point-slope form is , where m is the slope and is a point on the line of the equation

∵ The slope-intercept form of the equation of a line is y = 5x – 3

– Compare it with the slope- intercept form above

∴ m = 5 and b = -3

∵ The line passes through point (-2 , -13) = -2 and = -13

∵ The slope of the line m = 5

– Substitute these values in the point-slope form above

∴ y – (-13) = 5(x – (-2))

y + 13 = 5(x + 2)

To check your answer let us change it to the slope intercept form

∵ y + 13 = 5(x + 2)

– Simplify the right hand side

∴ y + 13 = 5(x) + 5(2)

∴ y + 13 = 5x + 10

– Subtract 13 from both sides

∴ y = 5x – 3 ⇒ same given equation

The point-slope form of the equation for this line is y + 13 = 5(x + 2)