Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.

Question

x-intercept: -2

 

y-intercept: 10

 

Give point-slope form and slope intercept form

Answer 1

Let's start by finding the slope of this line. If the x-intercept is -2, then then line crosses the x-axis when x = -2. That means the coordinates of that point is (-2, 0). The y-intercept is 10, so the coordinates are (0, 10).

Use those two points to find the slope using Δy / Δx .

m = y₁-y₂ / x₁-x₂

m = 0 - 10 / -2 - 0

m = -10 / -2

m = 5

Point slope formula is y - y₁ = m (x - x₁). m is the slope, which we just found out, and y1 and x1 are the coordinates of any point on the line. So if we choose (-2, 0) and plug it into the equation, we get:

y - 0 = 5 (x - -2)

We could also use the other coordinate to get:

y - 10 = 5 (x - 0)

Both of these equations are equal to each other (simplify them if you don't believe me!)

Slope intercept form is y = mx + b, where b is the y-intercept. We already know m, and the y-intercept is given as 10, so plug them in and we get:

y = 5x + 10

Answer 2

So, you have 2 points, (-2,0) and (0,10)

m = (-2 - 0)/(0 - 10) = -2/-10 = 1/5

Now, use either point.

y - 0 = (1/5)(x - (-2))

y = (1/5)x + 2/5