Interpret Linear Function Equations - 8th Grade Math

$(0,1),(1,3),(2,5)$. Check if slope is constant between all pairs.

$m=rac{11-2}{4-1}=3$. Use the slope formula with the given points.

$m=0$. Horizontal lines have no change in y.

$(0,b)$. When $x=0$, $y=b$ in the equation.

$b=5$. The constant term is the y-intercept.

$A=s^2$. Squaring the input makes it nonlinear.

$b=-5$. The y-intercept is the y-value at $x=0$.

Yes; the slope is constant ($m=2$). Calculate slopes: all equal $2$.

$y = -rac{1}{2}x + 3$. First-degree equations have constant rates.

$y = rac{3}{x}$. Division by x creates a curve, not a line.

A straight line. Linear equations always produce straight lines.

$m$ is the slope (rate of change) of the line. It determines how steep the line is and its direction.

Yes; it is linear with $m=0$ and $b=7$. Horizontal lines are linear with zero slope.

$b$ is the $y$-intercept (the value of $y$ when $x=0$). It's where the line crosses the y-axis.

$y = 2x + 1$. Only first-degree equations are linear.

A function with a constant rate of change. The slope remains the same between any two points.

No; it is not linear. Powers greater than 1 create curves.

$y=5$. Substitute: $y = 2(3) - 1 = 6 - 1$.

Undefined slope. Vertical lines have infinite steepness, so slope is undefined.

$x=4$. Vertical lines have constant $x$-values.

$y=4$. Horizontal lines have constant $y$-values.

Not linear. The $x^2$ term makes it quadratic, not linear.

$m=-3$. The coefficient of $x$ in slope-intercept form is the slope.

$m=\frac{y_2-y_1}{x_2-x_1}$. Rise over run between any two points on the line.

A straight line. Linear functions always produce straight lines when graphed.

$m=3$. $\frac{19-7}{6-2}=\frac{12}{4}=3$

$b$ is the $y$-intercept (value when $x=0$). The point where the line crosses the y-axis.

$m$ is the slope (rate of change). It determines the steepness and direction of the line.

$m=0$. Horizontal lines have zero slope since $y$ doesn't change.