Question

Write an equation in point-slope form and in slope-intercept form. A line passes through (1, -5)* and (-3, 7) Write an equation for the line in point-slope form and rewrite the equation in slope-intercept form *this is the first point (x1, y1) plz show work

Answer 1

Point-slope form:

y - y₁ = m(x - x₁)

You need to find "m" which is the slope.

To do so, use the slope formula and plug in the two points:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(7-(-5))/(-3-1)`

`m=(7+5)/(-3-1) =(12)/(-4) =-3`

m = -3

(x₁ , y₁) = (1, -5)

Plug this into the equation:

y - y₁ = m(x - x₁)

y - (-5) = -3(x - 1)

y + 5 = -3(x - 1)

Slope-intercept form:

y = mx + b "m" is the slope, "b" is the y-intercept

In order to get the equation from point-slope form to slope-intercept form, isolate/get the "y" by itself.

y + 5 = -3(x - 1) First distribute/multiply -3 into (x - 1)

y + 5 = -3x + 3 Subtract 5 on both sides

y = -3x - 2