Question

graph the following features: - y-intercept = 1 - slope = 3

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given that the y - intercept $b = 1$ and the slope $m=3$, the equation of the line is $y=3x + 1$.

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. When $x = 0$, $y=1$. So we plot the point $(0,1)$ on the coordinate plane.

Step3: Use the slope to find another point

The slope $m = 3=\frac{\text{rise}}{\text{run}}=\frac{3}{1}$. From the point $(0,1)$, we move up 3 units (because the rise is 3) and then 1 unit to the right (because the run is 1). This gives us the point $(0 + 1,1+3)=(1,4)$. We can also move down 3 units and left 1 unit from $(0,1)$ to get another point $(- 1,1 - 3)=(-1,-2)$ (optional, but helps in drawing the line).

Step4: Draw the line

Connect the points $(0,1)$ and $(1,4)$ (and other points if needed) with a straight line to graph the linear function.

To graph the line with a y - intercept of 1 and a slope of 3:

1. Start by marking the point \((0, 1)\) on the y - axis (since the y - intercept is the value of \(y\) when \(x = 0\)).
2. Use the slope \(m=3=\frac{3}{1}\). From the point \((0,1)\), move 1 unit to the right (in the positive \(x\) - direction) and 3 units up (in the positive \(y\) - direction) to get the point \((1,4)\).
3. Draw a straight line passing through the points \((0,1)\) and \((1,4)\) (you can extend the line in both directions).

The equation of the line is \(y = 3x+1\) and its graph is a straight line passing through \((0,1)\) and having a "steep" positive slope (going up from left to right).

Answer:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given that the y - intercept $b = 1$ and the slope $m=3$, the equation of the line is $y=3x + 1$.

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. When $x = 0$, $y=1$. So we plot the point $(0,1)$ on the coordinate plane.

Step3: Use the slope to find another point

The slope $m = 3=\frac{\text{rise}}{\text{run}}=\frac{3}{1}$. From the point $(0,1)$, we move up 3 units (because the rise is 3) and then 1 unit to the right (because the run is 1). This gives us the point $(0 + 1,1+3)=(1,4)$. We can also move down 3 units and left 1 unit from $(0,1)$ to get another point $(- 1,1 - 3)=(-1,-2)$ (optional, but helps in drawing the line).

Step4: Draw the line

Connect the points $(0,1)$ and $(1,4)$ (and other points if needed) with a straight line to graph the linear function.

To graph the line with a y - intercept of 1 and a slope of 3:

1. Start by marking the point \((0, 1)\) on the y - axis (since the y - intercept is the value of \(y\) when \(x = 0\)).
2. Use the slope \(m=3=\frac{3}{1}\). From the point \((0,1)\), move 1 unit to the right (in the positive \(x\) - direction) and 3 units up (in the positive \(y\) - direction) to get the point \((1,4)\).
3. Draw a straight line passing through the points \((0,1)\) and \((1,4)\) (you can extend the line in both directions).

The equation of the line is \(y = 3x+1\) and its graph is a straight line passing through \((0,1)\) and having a "steep" positive slope (going up from left to right).