Question

Linear function k
has a zero of −3
and a y-intercept of 4
. Which graph best represents k
?(1 point)
Responses






Question
The graph of a linear function, f
, is shown.



What is the zero of f
?

(1 point)
Responses

4
4

2
2

-3
-3

-2
The graph of linear function g
passes through the points (−7,−4)
and (7, 6)
as shown.



What are the slope and y-intercept of the graph g
?

(1 point)
Responses

The slope is 57
and the y-intercept is -1
The slope is 5 sevenths and the y-intercept is -1

The slope is 57
and the y-intercept is 1
The slope is 5 sevenths and the y-intercept is 1

The slope is 75
and the y-intercept is -1
The slope is 7 fifths and the y-intercept is -1

The slope is 75
and the y-intercept is 1
Which equation best represents the line shown on the grid?



(1 point)
Responses

y = 3; undefined slope
y = 3; undefined slope

y = 3; zero slope
y = 3; zero slope

x = 3; undefined slope
x = 3; undefined slope

x = 3; zero slope
The graph of a linear function is shown on the grid.



Which equation is best represented by this graph?

(1 point)
Responses

y+2=75(x+7)
y plus 2 is equal to 7 fifths times open paren x plus 7 close paren

y−2=75(x−7)
y minus 2 is equal to 7 fifths times open paren x minus 7 close paren

y+2=57(x+7)
y plus 2 is equal to 5 sevenths times open paren x plus 7 close paren

y−2=57(x−7)

Answer 1

Let's go through each question one by one.

1. **Linear function k has a zero of -3 and a y-intercept of 4. Which graph best represents k?**
- The zero of the function means the point where the function crosses the x-axis, which is at \( x = -3 \). The y-intercept is where the function crosses the y-axis, which is at \( (0, 4) \). Therefore, we are looking for a line that passes through the point \( (0,4) \) and \( (-3, 0) \).

2. **What is the zero of the function f?**
- The zero of a function is the value of \( x \) for which \( f(x) = 0 \). You would need to determine where the graph crosses the x-axis to answer this. Look for the x-coordinate of the point where the graph meets the x-axis.

3. **What are the slope and y-intercept of the graph g, which passes through the points (−7,−4) and (7, 6)?**
To find the slope (m), use the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values:
\[
m = \frac{6 - (-4)}{7 - (-7)} = \frac{10}{14} = \frac{5}{7}
\]

To find the y-intercept (b), you can use the slope-intercept form \( y = mx + b \) and use one of the points to solve for b.

Using the point (7, 6):
\[
6 = \frac{5}{7}(7) + b
\]
\[
6 = 5 + b \implies b = 1
\]

Thus, the slope is \( \frac{5}{7} \) and the y-intercept is 1.

4. **Which equation best represents the line shown on the grid?**
- Without seeing the grid, I can’t determine the equation. However, if a line is horizontal (constant y-value), it has a zero slope. If it is vertical (constant x-value), it has an undefined slope. If you can identify the behavior of the line, you can answer accordingly.

5. **Which equation is best represented by this graph?**
- Again, without seeing the graph, it's tough to determine the best equation. You would look for an equation that matches the slope and y-intercept shown in the graph. For instance, if you found a slope of \( \frac{7}{5} \) and a point (like (7, 2)), you could use the point-slope form to write the equation.

Feel free to provide additional details or the specific graphs, and I can help with more precise answers!