Question

What is the slope-intercept equation for the line below?

Answer 1

y = $\frac{1}{2}$ x + 1

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 1 ) and (x₂, y₂ ) = (4, 3 ) ← 2 points on the line

m = $\frac{3-1}{4-0}$ = $\frac{2}{4}$ = $\frac{1}{2}$

the line crosses the y-axis at (0, 1 ) ⇒ c = 1

y = $\frac{1}{2}$ x + 1 ← in slope-intercept form

Answer 2

answer: y = x + 1

work:

use y = mx + b (slope-intercept form) to model the equation.

note: b = y-intercept and x = slope

the y intercept in this equation is (0, 1), or 1.

so, add that to your equation.

y = mx + 1.

we still need to find the slope. we can do this the easy way by inserting in y and y values and solving for m.

4 = m(3) + 1

work to isolate m.

start by subtracting 1 from each side.

3 = 3m

divide both sides by 3.

1 = m

your slope is one. insert that into the equation.

y = 1x + 1

since 1x and x are the same thing (because you are just multiplying x and 1) you can rewrite the equation as y = x + 1 to make it look neater.

i hope this helps, and have a great day! don't hesitate to ask if you need more help with this specific question! ♥ - eviezoom