Final answer:
The slope-intercept form of the equation is y = (7/3)x - 4. The standard form of the equation is 7x - 3y = -12.
Step-by-step explanation:
To find the slope-intercept form and standard form for the given points, we need to first find the slope between the two points. The formula for slope is given by:
slope (m) = (y2 - y1) / (x2 - x1)
Using the values from the given points, we have:
slope (m) = (2 - (-5)) / (2 - (-1)) = 7/3
To find the slope-intercept form, we can substitute the slope value and one of the point's coordinates into the equation y = mx + b. Using the point (-1, -5), we have:
y = (7/3)x + b
Substituting the x and y values and solving for b, we get:
-5 = (7/3)(-1) + b
Simplifying the equation, we get:
b = -4
Therefore, the slope-intercept form of the equation is:
y = (7/3)x - 4
To find the standard form of the equation, we can rearrange the slope-intercept form equation:
y = (7/3)x - 4
3y = 7x - 12
7x - 3y = -12
Learn more about Slope-Intercept Form