Finding the slope and y-intercept of a line given the graph
Answer:
[tex]b = 4[/tex]
[tex]m = -\frac{1}{3}[/tex]
Step-by-step explanation:
An equation of a line written in its Slope-intercept Form, [tex]y = mx +b[/tex], has [tex]b[/tex] as its [tex]y[/tex]-intercept and [tex]m[/tex] as its slope.
[tex]b[/tex] or the [tex]y[/tex]-intercept is the [tex]y[/tex]-coordinate when [tex]x = 0[/tex]. On the given line, we can see that when [tex]x = 0[/tex], [tex]y = 4[/tex]. It's [tex]y[/tex]-intercept is the point [tex](0,4)[/tex] so [tex]b = 4[/tex].
The slope, [tex]m[/tex], of the line can be calculated by [tex]\frac{y_2 -y_1}{x_2 -x_1}\\[/tex] where [tex]x_n[/tex] and [tex]y_n[/tex] is the [tex]xy[/tex]-coordinates of any point [tex]n[/tex] on the line. In the given line, we can see that [tex](5,3)[/tex] is on the line so this can be point [tex]1[/tex]. [tex](0,4)[/tex] is also on the line (yes, you can also use the [tex]y[/tex]-intercept in calculating the slope of the line) so this can be our point [tex]2[/tex].
[tex]m = \frac{4 -3}{0 -3} \\ m = \frac{1}{-3} \\ m = -\frac{1}{3}[/tex]
The [tex]y[/tex]-intercept is [tex]b = 4[/tex] and the slope is [tex]m = -\frac{1}{3}[/tex]
