write the slope-intercept form of the equation of the line through the given point with the given slope. through:(-1,-2), slope=6
first, use the point-slope form:
y+2 = 6(x+1)
Now move stuff around till you have y = mx+b
y+2 = 6(x+1)
y+2 = 6x+6
y = 6x+4
The slope-intercept form of an equation of a line is given by y = mx + b, where m represents the slope and b represents the y-intercept.
We are given the point (-1,-2) and the slope m = 6.
To find the equation of the line, we can substitute the values into the slope-intercept form:
y = 6x + b
To determine the value of b, we can use the coordinates of the given point (-1,-2). Substituting these values into the equation, we get:
-2 = 6(-1) + b
Simplifying:
-2 = -6 + b
To solve for b, we can add 6 to both sides:
-2 + 6 = b
4 = b
So, the equation of the line in slope-intercept form, through the point (-1,-2) with a slope of 6, is:
y = 6x + 4
To write the equation of a line in slope-intercept form, which is y = mx + b, we need to substitute the known values of the slope (m) and the given point (-1, -2) into the equation and solve for the y-intercept (b).
Given:
Point: (-1, -2)
Slope: 6
Substituting the slope and the coordinates of the point into the equation, we have:
-2 = 6(-1) + b
First, let's simplify the equation:
-2 = -6 + b
Next, let's solve for b, the y-intercept:
b = -2 + 6
b = 4
Now that we have found the value of b, we can write the equation in slope-intercept form:
y = mx + b
Substituting the values of m (slope) and b (y-intercept), we get:
y = 6x + 4
Therefore, the slope-intercept form of the equation of the line passing through the point (-1, -2) with a slope of 6 is y = 6x + 4.