Find the equation using point slope formula . Write the final equation in slope intercept form . (-3,7) and (-1,-5) are points on the line .
slope = m = (7 - -5) / (-3 - -1)
point-slope ... y + 5 = m (x + 1)
slope-intercept ... solve the point-slope equation for y
To find the equation of a line using the point-slope formula, we need a point on the line and the slope of the line.
First, let's find the slope of the line using the given points (-3,7) and (-1,-5). The slope (m) is given by:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates (-3,7) and (-1,-5) into the formula, we get:
m = (-5 - 7) / (-1 - (-3))
= (-5 - 7) / (-1 + 3)
= -12 / 2
= -6
Now that we have the slope (m), we can use the point-slope formula to find the equation of the line, which is:
y - y1 = m * (x - x1)
Substituting (-3,7) as the point and -6 as the slope, we get:
y - 7 = -6 * (x - (-3))
y - 7 = -6 * (x + 3)
y - 7 = -6x - 18
Next, we rewrite the equation in slope-intercept form (y = mx + b), where b is the y-intercept. To do this, we isolate the y-term:
y = -6x - 18 + 7
y = -6x - 11
Therefore, the final equation, in slope-intercept form, is y = -6x - 11.