write the slope intercept form of an equation of the line that passes through (-2,0) and is parallel to the graph of y=-3x-2
you want a slope of -3 passing through (-2,0)
So start with the point-slope form:
y-0 = -3(x+2)
Now just rearrange things as needed
or, you know it will be of the form y = -3x+b
so plug in (-2,0) and find the value of b.
To find the slope-intercept form of an equation for a line parallel to the graph of another line, we need two pieces of information: the slope of the given line and the coordinates of a point on the line we want to find the equation for.
Given that the given line has an equation of y = -3x - 2, we can determine the slope of this line. In slope-intercept form (y = mx + b), the number "m" represents the slope. In this case, the slope is -3.
Now, we know the slope of the line we want to find the equation for is -3. Additionally, we're given a point on the line (-2, 0).
We can substitute the values we have into the point-slope form of the equation and then simplify it to the slope-intercept form.
The point-slope form of an equation is: y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line and "m" is the slope.
Substituting the given values, we have:
y - 0 = -3(x - (-2))
Simplifying further:
y - 0 = -3(x + 2)
y = -3x - 6
Therefore, the slope-intercept form of the equation for the line passing through (-2, 0) and being parallel to the graph of y = -3x - 2 is y = -3x - 6.