Point-slope form requires that we have the slope and a point on the line. Recall that the y𝑦-intercept is where the graph crosses the y𝑦-axis and we can write it as a coordinate point. The y𝑦-intercept of this equation is −3−3 so the coordinate point would be:(( ,, ))We now have the slope and a point on the line so we can write an equation in point-slope form.y−3=4(x−0)
Question
Point-slope form requires that we have the slope and a point on the line. Recall that the y𝑦-intercept is where the graph crosses the y𝑦-axis and we can write it as a coordinate point. The y𝑦-intercept of this equation is −3−3 so the coordinate point would be:(( ,, ))We now have the slope and a point on the line so we can write an equation in point-slope form.y−3=4(x−0)
Solution
The point-slope form of a linear equation is given by y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
In the given equation, the slope (m) is 4 and the y-intercept is -3. The y-intercept is the point where the line crosses the y-axis, which always has an x-coordinate of 0. Therefore, the point on the line that we have is (0, -3).
Substituting these values into the point-slope form gives us:
y - (-3) = 4(x - 0)
Simplifying this gives us:
y + 3 = 4x
This is the equation of the line in point-slope form.
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