PCC SLC Math Resources

The rise would be \(6\text{.}\)

All lines with positive slope increase (go upward) from left-to-right whereas all lines with negative slope decrease (go downward) from left-to-right. All lines with a slope of zero are horizontal. Although you can't verify it with the Desmos graph, vertical lines have no slope (sometimes stated as an undefined slope).

The slope is \(\frac{3}{2}\text{.}\)

The slope is \(-\frac{5}{4}\text{.}\)

The \(y\)-intercept is \((0,2)\text{.}\)

The \(y\)-intercept is \((0,-3)\text{.}\)

The equation is \(y=\frac{3}{2}x+2\text{.}\)

The equation is \(y=-\frac{5}{4}x-3\text{.}\)

We begin by using the formula \(m=\frac{y_2-y_1}{x_2-x_1}\text{.}\)

\(m=\frac{3-(-2)}{0-2}=-\frac{5}{2}\)

We know that the \(y\)-intercept is \((0,3)\text{,}\) so the slope-intercept equation for the line is \(y=-\frac{5}{2}x+3\text{.}\)

We begin by using the formula \(m=\frac{y_2-y_1}{x_2-x_1}\) to determine that the slope of the line is \(-3\text{.}\)

We don't directly know the \(y\)-intercept of the line, but from the slope we know that the equation of the line is \(y=-3x+b\) where \(b\) is the \(y\)-coordinate of the \(y\)-intercept. Substituting the coordinates of the ordered pair \((2,-7)\) into that equation gives us \(-7=(-3)(2)+b\text{,}\) and solving for \(b\) we get \(-1\text{,}\) so the slope-intercept equation for the line is \(y=-3x-1\text{.}\) Note that we could also have used the ordered pair \((-3,8)\) to determine the value of \(b\text{.}\)

We begin by using the formula \(m=\frac{y_2-y_1}{x_2-x_1}\) to determine that the slope of the line is \(-\frac{1}{2}\text{.}\)

We don't directly know the \(y\)-intercept of the line, but from the slope we know that the equation of the line is \(y=-\frac{1}{2}x+b\) where \(b\) is the \(y\)-coordinate of the \(y\)-intercept. Substituting the coordinates of the ordered pair \((5,1)\) into that equation gives us \(1=-\frac{1}{2}(5)+b\text{,}\) and solving for \(b\) we get \(b=\frac{7}{2}\text{,}\) so the slope-intercept equation for the line is \(y=-\frac{1}{2}x+\frac{7}{2}\text{.}\) Note that we could also have used the ordered pair \((-3,5)\) to determine the value of \(b\text{.}\)

The equation of the line is \(y=4x+3\text{.}\)

The line that passes through the first two points has a slope of \(\frac{5}{3}\) whereas the line that passes through the first and third point has a slope of \(2\text{.}\) If the points all lied on the same line, we would get the same slope no matter which two points we used in the slope formula.