The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the point (7, -3) and y-intercept = 2. Therefore we have:
[tex]y=mx+2[/tex]
Substitute the coordinates of the point to the equation of line:
[tex]-3=7m+2[/tex] subtract 2 from both sides
[tex]-5=7m[/tex] divide both sides by 7
[tex]-\dfrac{5}{7}=m\to m=-\dfrac{5}{7}[/tex]
Therefore we have:
[tex]y=-\dfrac{5}{7}x+2[/tex] multiply both sides by 7
[tex]7y=-5x+14[/tex] add 5x to both sides
[tex]5x+7y=14[/tex]
The equation in standard form is -5x - 7y = -14
The slope intercept form is as follows:
y = mx + b
where
m = slope
b = y-intercept
Therefore,
b = 2
y = mx + 2
y = m(0) + 2
y = 2
(0, 2)
let's find the slope using the 2 coordinates
(0, 2)(7, -3)
m = -3 - (2) / 7 -0 = - 5 / 7
y = -5 / 7 x + 2
multiply through by 7
7y = -5x + 14
In standard form it will be as follows:
-5x - 7y = -14
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