Answer:
Use point slope form, by finding the slope between two of the points given on the line you can then input it with one of the points into the formula. Then simplify to convert to slope-intercept form. You can then graph it easily. After which, you can convert to standard form by getting the variables to one side. Be sure in standard form to clear negatives x may have or any fractions x or y may have through multiplication.
Step-by-step explanation:
To write an equation for linear equations, we use one of three forms: standard, slope intercept, and point slope. Slope intercept and point slope are the most common. After we choose our form, we need to find the information required for that form. Point slope is easiest since it requires the slope/rate of change and any point on the line.
Point slope:[tex]y-y_1=m(x-x_1)[/tex]
We must find the slope using the slope formula.
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=-3\\y_1=1[/tex] and [tex]x_2=3\\y_2=5[/tex]
[tex]m=\frac{5-1}{3-(-3)}[/tex]
[tex]m=\frac{4}{3+3}=\frac{4}{6} =\frac{2}{3}[/tex]
We will substitute [tex]m=\frac{2}{3}[/tex] and [tex]x_1=-3\\y_1=1[/tex].
[tex]y-1=\frac{2}{3} (x-(-3))[/tex]
We can simplify to get slope intercept form:
[tex]y-1=\frac{2}{3} (x+3))[/tex]
[tex]y-1=\frac{2}{3}x+\frac{2}{3}(3)[/tex]
[tex]y-1=\frac{2}{3}x+2[/tex]
[tex]y-1+1=\frac{2}{3}x+2+1[/tex]
[tex]y=\frac{2}{3}x+3[/tex]
This is the slope intercept form. We can graph it by finding 3 on the y-axis. Plot a point there. Then move up two units and to the right three units. Plot a point. Connect the points.
To convert to Standard Form, we will rearrange the equation with x and y on the same side.
[tex]y=\frac{2}{3}x+3[/tex]
[tex]-\frac{2}{3}x+y=\frac{2}{3}x-\frac{2}{3}x+3[/tex]
[tex]-\frac{2}{3}x+y=3[/tex]
[tex]-3(-\frac{2}{3}x+y=3)[/tex]
[tex] 2x-3y=-9[/tex]
This is the standard form.
