Question

4.5 slope intercept form
question 7 of 15 (1 point) | question attempt: 1 of 3
amount of battery charge (%)
time (hours)
write a linear equation to represent the relationship between x and y.
y = 10x + 30

Explanation:

Step1: Identify the 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.

Step2: Determine the y - intercept

From the graph, when $x = 0$ (the y - intercept), the value of $y$ (battery charge) is 30. So, $b = 30$.

Step3: Calculate the slope

To find the slope $m$, we can use the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points. When $x = 0$, $y = 30$; when we look at the graph, if we assume another point, for example, when $x = 1$, from the line, the $y$ - value seems to be $30 + 10=40$ (since the line is increasing). So, using the points $(0,30)$ and $(1,40)$, the slope $m=\frac{40 - 30}{1 - 0}=\frac{10}{1}=10$.

Step4: Write the equation

Substituting $m = 10$ and $b = 30$ into the slope - intercept form $y=mx + b$, we get $y = 10x+30$.

Answer:

$y = 10x + 30$