Answer:
y = [tex]\frac{4}{7}[/tex]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 [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1}}[/tex]. It doesn't matter which set of coordinates is which pair.
(x₁,y₁) = (7,4)
(x₂,y₂) = (0,0) a.k.a "the origin"
[tex]\frac{0-4}{0-7} = \frac{-4}{-7} = \frac{4}{7}[/tex] = 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 = [tex]\frac{4}{7}[/tex] (x - 7) Distribute
y - 4 = [tex]\frac{4}{7} x - \frac{4*7}{7}[/tex] Simplify
y - 4 = [tex]\frac{4}{7}x - 4[/tex] Add 4 to both sides
y = [tex]\frac{4}{7}[/tex]x + 0 or y = [tex]\frac{4}{7}[/tex]x
Check your work by plugging in your given coordinates:
y = [tex]\frac{4}{7}[/tex]x
0 = [tex]\frac{4}{7}[/tex](0)
0 = 0
and
y = [tex]\frac{4}{7}[/tex]x
4 = [tex]\frac{4}{7}[/tex](7)
4 = [tex]\frac{4*7}{7}[/tex]
4 = 4
