Final answer:
To write the equation of the line in slope-intercept form, we used the formula y = mx + b, replacing m with the slope (-6), and solving for b using the given point (-2,4), resulting in the equation y = -6x - 8.
Step-by-step explanation:
To write an equation in slope-intercept form for a line that passes through the point (-2,4) with a slope of -6, we use the formula y = mx + b, where m is the slope and b is the y-intercept.
Since we already have a point and the slope, we can find the y-intercept by plugging the values into the slope-intercept equation and solving for b.
Step 1: Substitute the point (-2,4) into the equation to get:
4 = (-6)×(-2) + b
Step 2: Simplify and solve for b:
4 = 12 + b
Step 3: Isolate b:
b = 4 - 12
b = -8
Now we have the y-intercept (b), so the slope-intercept form of the equation is:
y = -6x - 8