Grade 9 Math - Linear Equations Basics - Training Quiz

This equation is in the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept. By identifying \(b = -7\), we see that when \(x = 0\), the equation simplifies to \(y = -7\). Therefore, the \(y\)-intercept is \(-7\).

The slope of a line is calculated using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Substituting the given points, \(m = \frac{11 - 3}{6 - 2} = \frac{8}{4} = 2\). The slope is \(2\), which represents the rate of change in \(y\) for a unit change in \(x\).

To rewrite in slope-intercept form, isolate \(y\): \(2y = 6x + 10\), then divide by 2: \(y = 3x + 5\). The slope-intercept form is \(y = 3x + 5\), and the slope is \(3\).

Using the slope-intercept form \(y = mx + b\), substitute \(m = 2\) and \(b = -4\): \(y = 2x - 4\). This equation represents a line with the given slope and intercept.

Start with the point-slope form \(y - y_1 = m(x - x_1)\), where \(m = -3\) and \((x_1, y_1) = (1, 5)\). Substituting: \(y - 5 = -3(x - 1)\). Simplify: \(y - 5 = -3x + 3\). Adding 5: \(y = -3x + 8\).