Answer:
Point-slope form: [tex]y-1 = \frac{1}{5}(x-10)[/tex]
Slope intercept form: [tex]y = 0.2x -1[/tex]
Step-by-step explanation:
Point-slope form:
[tex]y-y_1 = m(x-x_1)[/tex]
y1 and x1 are the y and x coordinates for a point on the line.
m is the slope.
We know m, as it is given:
m = 1/5
We also know a point on the line, (10, 1).
Here, the x-coordinate is 10, and the y-coordinate is 1.
Thus we can say the following:
[tex]x_1 = 10\\y_1 = 1[/tex]
And, from previously:
[tex]m=\frac{1}{5}[/tex]
Let's put these values into our equation.
[tex]y-y_1 = m(x-x_1)[/tex]
[tex]y-1 = \frac{1}{5}(x-10)[/tex]
If we want to answer in slope-intercept form:
[tex]y=ax+b[/tex]
We can continue based on our point-form expression to isolate y:
[tex]y-1 = \frac{1}{5}(x-10)\\[/tex]
Add 1 to both sides:
[tex]y= \frac{1}{5}(x-10)+1[/tex]
Expanding the parenthesis (multiplying 1/5 with x and -10):
[tex]y= \frac{1}{5}x -2 + 1 \\\\y= \frac{1}{5}x -1\\\\y = 0.2x -1[/tex]
Point-slope form: [tex]y-1 = \frac{1}{5}(x-10)[/tex]
Slope intercept form: [tex]y = 0.2x -1[/tex]
