Question

Find the equation of the line with slope =10 and passing through (-6,7). Write your equation in point slope form AND slope intercept forms.

Answer 1

The equation of the line in the slope-point form is y - 7 = 10(x + 6)

The equation of the line in the slope-intercept form is y = 10x + 67

Explanation:

The slope-point form of the linear equation is y - y1 = m(x - x1), where

• m is the slope

• (x1, y1) are the point lies on the line

The slope-intercept form of the linear equation is y = m x + b, where

• m is the slope

• b is the y-intercept

∵ The slope of the line is 10

∴ m = 10

∵ The line passes through the point (-6, 7)

∴ x1 = -6 and y = 7

→ Substitute them in the slope-point form above

∵ y - 7 = 10(x - -6)

∵ (-)(-) = (+)

∴ y - 7 = 10(x + 6)

∴ The equation of the line in the slope-point form is y - 7 = 10(x + 6)

→ Substitute m in the slope-intercept form

∵ y = 10x + b

→ To find b substitute x by -6 and y by 7 in the equation

∵ 7 = 10(-6) + b

∴ 7 = -60 + b

→ Add 60 to both sides to find b

∴ 67 = b

→ Substitute the value of b in the equation

∴ y = 10x + 67

∴ The equation of the line in the slope-intercept form is y = 10x + 67