Question

find the slope intercept form for the equation of a line which passes through the point( 7, 4) and the origin​

Answer 1

Answer:

y = $\frac{4}{7}$x

Explanation:

Slope-intercept form is y = mx + b

m is the slope (rise over run)

b is the y-intercept (where the line crosses the y-axis)

To get the slope, use the formula $\frac{y_{2} - y_{1} }{x_{2} - x_{1}}$. It doesn't matter which set of coordinates is which pair.

(x₁,y₁) = (7,4)

(x₂,y₂) = (0,0)  a.k.a "the origin"

$\frac{0-4}{0-7} = \frac{-4}{-7} = \frac{4}{7}$ = your slope (m)

Now, to get to slope-intercept form, you have to plug what you know into point-slope form, y - y₁ = m(x - x₁).

y₁ = a point on the line

m = slope

x₁ = the matching coordinate to y₁

y - 4 = $\frac{4}{7}$ (x - 7)   Distribute

y - 4 = $\frac{4}{7} x - \frac{4*7}{7}$   Simplify

y - 4 = $\frac{4}{7}x - 4$   Add 4 to both sides

y = $\frac{4}{7}$x + 0 or y = $\frac{4}{7}$x

Check your work by plugging in your given coordinates:

y = $\frac{4}{7}$x

0 = $\frac{4}{7}$(0)

0 = 0

and

y = $\frac{4}{7}$x

4 = $\frac{4}{7}$(7)

4 = $\frac{4*7}{7}$

4 = 4