An equation in point-slope form follows a specific format.
y- y_1= m(x- x_1)
In this format, m represents the slope and the point ( x_1, y_1) lies on the graph of the line. Observing the given equation, we see that it would only take a minor adjustment for it to be in point-slope form.
Now let's compare this equation with the general form of an equation in point-slope form.
y- y_1&= m(x- x_1)
y- 4 &= 3(x-( -2))
From what we know, we can see that the given equation gives us the point ( -2, 4) and the slope 3. Using this point and the slope to determine another point on the graph, we will be able to sketch the graph of the line.
Extra
Converting to Slope-Intercept Form
We used the equation in point-slope form to draw the graph. Now, let's try to convert it to the slope-intercept form and then draw the graph. It might sound complicated, but it is not. First, we will recall that an equation in slope-intercept form follows a specific format.
y= mx+ b
Here, m is the slope and b is the y-intercept. Keeping this in mind let's try to convert our equation to slope-intercept form.
We found that the slope-intercept form of our equation is y=3x+10. Let's begin by plotting the y-intercept and then using the slope to plot another point.
Finally, we will draw a line passing through the two points and our graph will be ready.
