Answer:
y = x - 6
Step-by-step explanation:
You can write a linear equation in slope-intercept form which uses the equation y = mx + b.
"x" and "y", when substituted with a point (x,y), show if a point is on the line.
"m" is the slope, which is how steep the line is.
"b" is the y-intercept, which is where the line hits the y-axis.
First, we can find the slope by substituting the two points into this equation [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]. Choose which point is point 1 and point 2.
Point 1 (8, 2) x₁ = 8 y₁ = 2
Point 2 (7, 1) x₂ = 7 y₂ = 1
Substitute the information into the equation for slope.
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{1-2}{7-8}[/tex]
[tex]m=\frac{-1}{-1}[/tex]
[tex]m=1[/tex]
Since the slope is 1, we usually do not write it into the equation. The slope "1" means that "x" in the equation will multiply by 1. You don't need this because any number multiplied by 1 is itself, the same number.
Substitute any point (7, 1) and slope (m = 1) into slope-intercept form. Remember points are written (x, y), so substitute x = 7 and y = 1.
y = mx + b
1 = 7 + b Remember slope, "m", is 1, so we can ignore it.
1 - 7 = 7 - 7 + b Subtract 7 from both sides to isolate "b".
1 - 7 = b 7-7=0 cancelled out on the right
b = -6 Solved for "b", y-intercept
Substitute the slope (m = 1) and the y-intercept (b = -6) into slope-intercept form to write the equation.
y = mx + b
y = (1)x + (-6) Remember 1 for slope can be ignored. Adding -6 is the same as just subtracting 6.
y = x - 6 Equation of the line
