Question

Please help!! thank you

Answer 1

Hello!

The answers are:

a - It's a line graph, and we need to find its equation by finding first its axis intercepts.

b - We have the graph of the line, meaning that we have the slope, and intercepts information.

c - The first strategy we can try is using the first, identifyin the axis intercept components and write the simplest line equation.

Why?

Since we have the graph of the line, we can find all the information that we need to solve the problem. First, we need to find the axis intercepts of the line:

x-axis intercept:

At the x-axis intercept, the y coordinate will be equal to 0, from the graph we know that the x-axis intercept is : 1.5

So, the interception point will be (1.5,0)

y-axis intercept:

At the y-axis intercept, the x coordinate will be equal to 0, from the graph we know that the y-axis intercept is: -1

So, the interception point will be (0,-1)

Therefore, the interception points of the line are (1.5,0) and (0,-1)

Now, we have to write the slope equation of the line which is:

`y=mx+b`

Where m can be defined like:

`m=slope=(y2-y1)/(x2-x1)`

We can use the coordinates of any point of the line, for this case we will use the intercept points, so:

`m=(-1-0)/(0-1.5)=(-1)/(-1.5)=0.66=(2)/(3)`

The slope is positive(2/3), it means that the function (line) is increasing.

So, the equation of the line in slope-interception form will be:

`y=(2)/(3)x-1`

Have a nice day!