Question

topic 2 linear relationships
7 mario is painting a canvas with one color that he will use as a
background. he has already painted 5 square feet. the directions
on his paint container state that each pint of paint will cover
16 square feet of canvas.
a. write an equation that represents the number of square feet of
canvas covered, y, given x number of pints of paint used.
b. graph the equation.
c. identify the slope and y - intercept of the graph. explain what
each means in terms of the situation.
d. mario was able to cover 37 square feet of his canvas. how
many pints of paint did mario use?

Explanation:

Step1: Determine the linear equation

Since each pint of paint covers 16 square feet, the relationship is \(y = 16x\). The initial value (y - intercept) is 0 because when \(x = 0\) (no paint used), \(y=0\) (no area covered).

Step2: Graph the equation

To graph \(y = 16x\), we can use two points. When \(x = 0\), \(y = 0\) (point \((0,0)\)). When \(x = 1\), \(y = 16\) (point \((1,16)\)). Plot these points and draw a straight - line through them.

Step3: Identify slope and y - intercept

The equation is in the form \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y = 16x+0\), the slope \(m = 16\) and the y - intercept \(b = 0\). The slope \(16\) means that for every 1 pint of paint (\(x\) increases by 1), the area covered (\(y\)) increases by 16 square feet. The y - intercept \(0\) means that when no paint is used (\(x = 0\)), no area is covered (\(y = 0\)).

Step4: Find the number of pints when \(y = 37\)

We use the equation \(y = 16x\). Substitute \(y = 37\) into the equation: \(37=16x\). Solve for \(x\): \(x=\frac{37}{16}=2.3125\)

Answer:

a. The equation is \(y = 16x\).
b. Graph with points \((0,0)\) and \((1,16)\) connected by a straight line.
c. Slope \(m = 16\) (16 square feet per pint of paint), y - intercept \(b = 0\) (no area covered with 0 pints).
d. Mario used \(2.3125\) pints of paint.