Question

what would the graph of 10x + 7y < 49 look ?

Answer 1

Answer: The graph is attached.

Step-by-step explanation:

1. Solve for y, as following:

$10x+7y<49\\7y<-10x+49\\y<-\frac{10}{7}x+\frac{49}{7}\\\\y<-\frac{10}{7}x+7$

2. The equation of the line in slope intercept form is:

$y=mx+b$

Where m is the slope and b is the y-intercept.

3. In this case the equation of the line is:

$y=-\frac{10}{7}x+7$

then:

$m=-\frac{10}{7}\\\\b=7$

4. Find the x-intercept. Make y=0. Then:

$0=-\frac{10}{7}x+7\\\frac{10}{7}x=7\\x=4.9$

5. Then, plot the line that passes through the points (0,7) and (4.9, 0).

6. The symbol of the inequality is < therefore, the line must be dashed and indicates that the region under the line must be shaded.

Then you obtain the graph attached.

Answer 2

Answer:

We need to graph the given inequality 10x + 7y < 49.

We can do that into 2 parts:

Part 1:

Graph the line 10x+7y=49

plug any number for x say x=0

10x+7y=49

10(0)+7y=49

0+7y=49

7y=49

y=49/7

y=7

hence it passes through point (0,7)

similarly plug y=0

10x+7(0)=49

10x=49

x=49/10

x=4.9

hence it passes through point (4.9,0)

Graph both points then join them by a straight dotted line because of < sign.

PART 2:

Shade the graph for inequality sign <

use any test point which is not on the given line say (0,0)

plug into original problem

10x + 7y < 49

10(0) + 7(0) < 49

0<49 is true

so shade in direction of test point

Hence final graph looks like: