Question

for the data given below, answer parts (a) through (d)

x	-19	-16	-14	-13	-9
y	102	122	120	132	142

...
y = 4x + 178
(type your answer in slope - intercept form. use integers or fractions for any numbers in the expression.)
(b) draw a scatter plot and the line found in part (a) on the same axes.
choose the correct graph below
○ a.
○ b.
○ c.
○ d.
help me solve this view an example get more help

Explanation:

Step1: Analyze the line equation

The line equation is \( y = 4x + 178 \). The slope \( m = 4 \) (positive), so the line should be increasing (going up from left to right). The y - intercept is \( 178 \), which is positive.

Step2: Analyze the scatter plot data

The \( x \)-values are negative (\(-19, - 16, -14, -13, -9\)) and \( y \)-values are positive (\(102, 122, 120, 132, 142\)). Let's check the slope direction: as \( x \) increases (becomes less negative), \( y \) should increase (since slope is positive).

Step3: Evaluate the graphs

• Graph A: Line is decreasing (negative slope) - incorrect.
• Graph B: Line is decreasing (negative slope) - incorrect.
• Graph C: Line is increasing, but let's check the y - intercept. The line in C seems to have a non - 178 y - intercept (visually) and the scatter plot points don't align well.
• Graph D: Line has a positive slope (increasing), and the scatter plot points (with negative \( x \) and positive \( y \)) should lie close to this line. Also, the slope and intercept match the equation \( y = 4x+178 \) (for \( x=-25 \), \( y = 4\times(-25)+178=78 \), and the line in D seems to pass through appropriate points).

Answer:

D