Graph the line with slope - 2 passing through the point (4, - 3).

Answer 1

We know that the slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We also know that the line has a slope of -2 and passes through the point (4, -3).

To find the equation of the line, we can plug in the values of m and x and y for the point we know:

-3 = (-2)(4) + b

-3 = -8 + b

b = 5

So the equation of the line is y = -2x + 5.

To graph the line, we can plot the y-intercept (0, 5) and then use the slope to find additional points. We can start at the y-intercept and move down 2 units and right 1 unit to get the point (1, 3). We can repeat this process to get additional points (-1, 7), (2, 1), and so on.

Alternatively, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

We can plug in the values we know:

y - (-3) = -2(x - 4)

y + 3 = -2x + 8

y = -2x + 5

This is the same equation we found before.