Given:
Point 1 → (-5, 0.6)
Point 2 → (5, -2.4)
Find: the equation of the line and its graph
Solution:
To help us determine the equation of the line passing through the given points, let's use the Two-Point Form formula.
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Let's plug into the formula above the coordinates of the two points.
[tex]y-0.6=\frac{-2.4-0.6}{5-(-5)}(x-(-5))[/tex]
Then, solve.
[tex]y-0.6=\frac{-3}{10}(x+5)[/tex]
Multiply -3/10 by the terms inside the parenthesis.
[tex]y-0.6=-\frac{3}{10}x-1.5[/tex]
Add 0.6 on both sides of the equation.
[tex]y-0.6+0.6=-\frac{3}{10}x-1.5+0.6[/tex][tex]\begin{gathered} y=-\frac{3}{10}x-0.9 \\ or \\ y=-0.3x-0.9 \end{gathered}[/tex]
Hence, the equation of the line passing through the given points in slope-intercept form is y = -0.3x - 0.9.
In the equation, the slope is -3/10 while the y-intercept is -0.9.
Since the slope is negative, the line must be leaning to the left. Since the y-intercept is -0.9, the line must cross the y-axis or the vertical line at -0.9. Hence, the graph of the equation is:
