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)

1 answer

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!